Boundary crossing probabilities and statistical applications. (English) Zbl 0632.62077

Siegmund, David

Ann. Stat. 14, 361-404 (1986).

Author’s summary: This paper surveys recent results involving boundary crossing probabilities and related statistical applications. The first part is concerned with problems of sequential analysis, especially repeated significance tests and their application to sequential clinical trials involving survival data.
The second part develops the probability theory motivated by the problems of Part 1. A method for computing first passage distributions of Brownian motion to linear boundaries is introduced and then modified to handle problems in discrete time and those involving nonlinear boundaries.
The third part is concerned with fixed sample statistical problems, especially change-point problems, which involve boundary crossing probabilities. Examples are given of problems for which the methods of Part 2 appear adequate and of problems which require new methods.

Reviewer: A.K.Basu

MSC:

62L10	Sequential statistical analysis
60J65	Brownian motion
60J50	Boundary theory for Markov processes

Keywords:

large deviations; recent results; boundary crossing probabilities; repeated significance tests; sequential clinical trials; survival data; first passage distributions of Brownian motion; linear boundaries; discrete time; nonlinear boundaries; fixed sample statistical problems; change-point problems